Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9751	(2^230746+3114)/2	69462	Stefano Morozzi	01/2020
9752	5^99359-2^99360	69449	Mike Oakes	12/2010
9753	(29*2^230684+1)/1395	69442	Lelio R Paula	08/2012
9754	17692^8411+8411^17692	69439	Hans Havermann	09/2019
9755	(2^230638+1278)/2	69429	Stefano Morozzi	01/2020
9756	(19*10^69424+77)/3	69425	Robert Price	08/2016
9757	(2^230610+1222)/2	69421	Stefano Morozzi	01/2020
9758	19^54287-96	69420	Lelio R Paula	09/2013
9759	20739^2222+2222^20739	69409	Hans Havermann	09/2019
9761	2^230541+58905	69400	Lelio R Paula	04/2012
9760	(2^230540+2818)/2	69400	Stefano Morozzi	01/2020
9762	2^230506+12705	69390	Lelio R Paula	02/2013
9763	8*6^89156-5	69378	Lelio R Paula	09/2014
9764	(18815^16231-1)/18814	69376	Serge Batalov	08/2020
9765	(2^230443+3594)/2	69370	Stefano Morozzi	01/2020
9766	2^230438-111347	69369	Enzo Doria	05/2014
9767	(2^230434+3150)/2	69368	Stefano Morozzi	01/2020
9768	2^230428-99	69366	Lelio R Paula	02/2012
9769	(62^38699+1)/63	69362	Paul Bourdelais	08/2017
9770	(2^230413+3090)/2	69361	Stefano Morozzi	01/2020
9771	3*10^69354+17	69355	Robert Price	03/2017
9772	(493*10^69340-7)/9	69342	Robert Price	07/2016
9773	(2^230325+590)/2	69335	Stefano Morozzi	01/2020
9775	(41*10^69321+373)/9	69322	Robert Price	04/2017
9774	(2^230282+1990)/2	69322	Stefano Morozzi	01/2020
9776	6^89072+53	69312	Lelio R Paula	09/2013
9777	155^31639+2	69300	Lelio R Paula	05/2013
9778	(2^230117+3462)/2	69272	Stefano Morozzi	01/2020
9779	(16941^16381-1)/16940	69271	Serge Batalov	08/2020
9780	3*7^81965-4	69269	Lelio R Paula	09/2014
9781	(16*10^69265+41)/3	69266	Robert Price	10/2017
9782	(86*10^69260-77)/9	69261	Robert Price	05/2016
9783	9*5^99087+4	69260	Lelio R Paula	09/2014
9784	3^145145+2660	69252	Lelio R Paula	09/2013
9785	11^66492-1140	69245	Enzo Doria	11/2012
9786	5*3^145129-4	69245	Lelio R Paula	04/2014
9787	7*3^145126+8	69244	Lelio R Paula	04/2014
9788	11^66480-2370	69232	Enzo Doria	12/2012
9789	(2^229965+3482)/2	69227	Stefano Morozzi	01/2020
9790	(2^229968+3010)/2	69227	Stefano Morozzi	01/2020
9791	(22589^15901-1)/22588	69227	Serge Batalov	08/2020
9792	2^229962-65	69226	Lelio R Paula	02/2012
9793	2^229958-110733	69225	Enzo Doria	05/2014
9794	V(332407)	69225	Serge Batalov	03/2015
9795	6^88959+7	69224	Lelio R Paula	09/2013
9796	15^58855-94	69219	Lelio R Paula	09/2013
9797	(2^229941+774)/2	69219	Stefano Morozzi	01/2020
9798	(2^229931+3270)/2	69216	Stefano Morozzi	01/2020
9799	159773#-p(159773)	69212	Henri Lifchitz	12/2018
9800	20223^2638+2638^20223	69189	Hans Havermann	09/2019
9802	(2^229838+47)/12081	69185	Lelio R Paula	04/2012
9801	(2^229828+3810)/2	69185	Stefano Morozzi	01/2020
9803	3^144952+98	69160	Lelio R Paula	09/2013
9804	5^98941-72	69157	Lelio R Paula	06/2013
9805	63329!4+256	69147	Robert Price	09/2019
9806	16422^16229+16229^16422	69142	Hans Havermann	09/2019
9807	(17*2^229604-1)/229	69117	Lelio R Paula	01/2014
9808	2^229585-1063	69112	Yves Minet	11/2012
9809	(13*2^229567-1)/19	69107	Lelio R Paula	01/2014
9810	(2^229419+1946)/2	69062	Stefano Morozzi	01/2020
9811	(2^229399+1890)/2	69056	Stefano Morozzi	01/2020
9812	(13*2^229393-1)/5	69055	Lelio R Paula	01/2014
9813	(2^229388+3666)/2	69053	Stefano Morozzi	01/2020
9814	(53*10^69050-17)/9	69051	Robert Price	09/2015
9815	(3887^19237-1)/3886	69050	Serge Batalov	08/2020
9816	(43*10^69048+47)/9	69049	Robert Price	12/2017
9817	(6420^18131-1)/6419	69031	Serge Batalov	08/2020
9818	2^229305-1868533	69028	Enzo Doria	04/2016
9819	2^229297+1385	69026	Lelio R Paula	04/2012
9820	18^54986-2441	69023	Enzo Doria	03/2013
9821	(34*10^69021-7)/9/3/67	69020	Makoto Morimoto	04/2016
9822	5^98736-14636	69014	Enzo Doria	02/2013
9823	(2^229252+2346)/2	69012	Stefano Morozzi	01/2020
9825	(13^61949-5^61949)/8	69007	Robert Price	03/2013
9824	(2^229235+2966)/2	69007	Stefano Morozzi	01/2020
9826	(2^229227+5)/611	69002	Lelio R Paula	04/2012
9827	2^229216-113279	69001	Enzo Doria	07/2014
9828	10^68994+51913	68995	Patrick De Geest	03/2016
9830	10^68994-10^5814-1	68994	Serge Batalov	01/2011
9829	10^68994-82947	68994	Patrick De Geest	03/2016
9831	(2^229182+814)/2	68991	Stefano Morozzi	01/2020
9833	(17*2^229136-1)/2381	68975	Lelio R Paula	01/2014
9832	(6081^18229-1)/6080	68975	Serge Batalov	08/2020
9834	2^229113+107	68970	Lelio R Paula	02/2012
9835	16877^12198+12198^16877	68965	Hans Havermann	09/2019
9836	(2^229056+2010)/2	68953	Stefano Morozzi	01/2020
9837	11^66202-4410	68943	Enzo Doria	01/2013
9838	12^63883+5	68942	Lelio R Paula	07/2013
9840	(9913*2^229002-1)/399903	68935	Lelio R Paula	04/2015
9839	(2^228997+2454)/2	68935	Stefano Morozzi	01/2020
9841	(2^228982+3118)/2	68931	Stefano Morozzi	01/2020
9842	(2^228982+3490)/2	68931	Stefano Morozzi	01/2020
9843	2^228962-111581	68925	Enzo Doria	05/2014
9844	2^228944+81	68920	Henri Lifchitz	01/2007
9845	11^66174-54	68914	Lelio R Paula	09/2013
9846	(2^228926+694)/2	68914	Stefano Morozzi	01/2020
9847	16756^12959+12959^16756	68911	Hans Havermann	09/2019
9848	2^228913-111265	68910	Enzo Doria	05/2014
9849	18917^4392+4392^18917	68909	Hans Havermann	09/2019
9851	2^228902+73519	68907	Enzo Doria	04/2016
9850	(2^228903+3018)/2	68907	Stefano Morozzi	01/2020
9852	(2^228892+3046)/2	68904	Stefano Morozzi	01/2020
9853	(47*2^228884+1)/63	68901	Lelio R Paula	04/2015
9854	(2^228857+3782)/2	68893	Stefano Morozzi	01/2020
9855	(20337^15991-1)/20336	68890	Serge Batalov	08/2020
9856	16542^14591+14591^16542	68883	Hans Havermann	09/2019
9857	2^228821+76427	68882	Enzo Doria	05/2016
9858	(2^228798+442)/2	68875	Stefano Morozzi	01/2020
9859	(2^228784+1222)/2	68871	Stefano Morozzi	01/2020
9860	3^144340+50	68868	Lelio R Paula	09/2013
9861	(2^228766+3850)/2	68866	Stefano Morozzi	01/2020
9862	2^228758-112967	68864	Enzo Doria	06/2014
9863	2^228743-111379	68859	Enzo Doria	05/2014
9864	2^228741-110911	68858	Enzo Doria	05/2014
9866	lucasU(1926,1,20964)-lucasU(1926,1,20963)	68857	Mike Oakes	05/2009
9865	3*5^98511-8	68857	Lelio R Paula	09/2014
9867	2^228717+467	68851	Lelio R Paula	02/2011
9868	(2^228714+2110)/2	68850	Stefano Morozzi	01/2020
9870	Phi(153218,10)/2211855049/23592660859/497714117291	68849	Maksym Voznyy	10/2011
9869	(32933^15241-1)/32932	68849	Serge Batalov	08/2020
9871	(2^228704+3990)/2	68847	Stefano Morozzi	01/2020
9872	(509203*2^228665-1)/35	68840	Lelio R Paula	04/2015
9873	(2^228648+2910)/2	68830	Stefano Morozzi	01/2020
9874	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
9875	(2^228580+3762)/2	68810	Stefano Morozzi	01/2020
9876	11^66074-1050	68809	Enzo Doria	11/2012
9877	(68*10^68798-11)/3	68800	Robert Price	10/2017
9878	2^228484+181	68781	Lelio R Paula	02/2012
9879	2^228479-58695	68780	Lelio R Paula	04/2012
9880	2^228465-15853	68775	Enzo Doria	04/2013
9881	11^66040-5400	68774	Enzo Doria	01/2013
9882	(13*2^228441-1)/575	68766	Lelio R Paula	01/2014
9883	(12170^16831-1)/12169	68756	Serge Batalov	08/2020
9884	(5683^18313-1)/5682	68754	Serge Batalov	08/2020
9885	(17*2^228393+1)/295	68752	Lelio R Paula	08/2012
9886	17859^7072+7072^17859	68749	Hans Havermann	09/2019
9887	(2^228368+1950)/2	68746	Stefano Morozzi	01/2020
9888	2*10^68744+41	68745	Robert Price	01/2017
9889	11^66011-150	68744	Enzo Doria	08/2012
9890	(2^228307+3570)/2	68727	Stefano Morozzi	01/2020
9891	(13*2^228304-1)/81	68726	Lelio R Paula	01/2014
9892	2^228295-111079	68724	Enzo Doria	05/2014
9894	(3^144039+7)/22	68723	Lelio R Paula	04/2012
9893	(8*10^68722+49)/3	68723	Robert Price	03/2016
9895	(35*10^68718+1)/9	68719	Serge Batalov	11/2010
9896	2^228271-228271	68717	Henri Lifchitz	11/2004
9897	2^228257+82875	68713	Lelio R Paula	02/2013
9898	3^144013+40	68712	Lelio R Paula	09/2013
9899	13^61671-86	68699	Lelio R Paula	09/2013
9900	(46*10^68698+683)/9	68699	Robert Price	12/2017
9901	17^55828-72	68694	Lelio R Paula	09/2013
9902	18675^4762+4762^18675	68683	Hans Havermann	09/2019
9903	6^88259+61	68679	Lelio R Paula	09/2013
9904	18^54699-5	68663	Lelio R Paula	09/2013
9905	33^45216+2	68662	Lelio R Paula	05/2013
9907	(2^228073-5)/3	68657	Lelio R Paula	04/2012
9906	(2^(6*38012+1)-5)/3	68657	Kevin Acres	11/2013
9908	(17929^16141-1)/17928	68653	Serge Batalov	08/2020
9909	2^228055-111607	68652	Enzo Doria	05/2014
9910	2^228054-114761	68652	Enzo Doria	05/2015
9911	2^228041+1185	68648	Lelio R Paula	04/2012
9912	2^228040-1037	68647	Yves Minet	11/2012
9913	2*F(328450)-1	68642	Henri Lifchitz	12/2009
9914	5^98201-34	68640	Lelio R Paula	06/2013
9915	(2^227993+1682)/2	68633	Stefano Morozzi	01/2020
9916	(2^227989+842)/2	68632	Stefano Morozzi	01/2020
9917	(2^227989+2010)/2	68632	Stefano Morozzi	01/2020
9918	(2^227959+3614)/2	68623	Stefano Morozzi	01/2020
9919	(2^227961+2054)/2	68623	Stefano Morozzi	01/2020
9920	9^71910+38^71910-24^71910-3*2^71910	68620	Mike Oakes	12/2010
9921	(2^227938+3678)/2	68616	Stefano Morozzi	01/2020
9922	18177^5948+5948^18177	68607	Hans Havermann	09/2019
9923	(29257^15361-1)/29256	68602	Serge Batalov	08/2020
9924	(2^227869+2822)/2	68596	Stefano Morozzi	01/2020
9925	(25910^15541-1)/25909	68586	Serge Batalov	08/2020
9926	(29779^15331-1)/29778	68586	Serge Batalov	08/2020
9927	(2^227813+666)/2	68579	Stefano Morozzi	01/2020
9928	7*2^227780-3	68570	Lelio R Paula	04/2014
9929	15327^16382-16382^15327	68567	Norbert Schneider	11/2018
9930	(2^227771+2730)/2	68566	Stefano Morozzi	01/2020
9931	2^227733-121	68555	Lelio R Paula	02/2012
9932	16460^14607+14607^16460	68549	Hans Havermann	09/2019
9933	2^227702-16967	68546	Enzo Doria	05/2013
9934	2^227689-111655	68542	Enzo Doria	05/2014
9935	gcd(V(823915),5F(164783)(F(164783)-1)+1)	68536	Serge Batalov	04/2015
9936	5^98051+2	68535	Ray Chandler	07/2011
9937	5*10^68524+51	68525	Robert Price	01/2017
9938	(11*10^68520-149)/3	68521	Robert Price	01/2017
9939	16624^13235+13235^16624	68520	Hans Havermann	09/2019
9940	16359^15430+15430^16359	68518	Hans Havermann	08/2019
9941	19^53573-78	68507	Lelio R Paula	09/2013
9942	(68*10^68504+13)/9	68505	Ray Chandler	10/2010
9943	9*5^98003+4	68503	Lelio R Paula	09/2014
9944	21121^1750+1750^21121	68497	Hans Havermann	10/2019
9945	2^227528+51	68493	Lelio R Paula	02/2012
9946	(146*28^47316+1)/3	68476	Karsten Bonath	06/2018
9947	(2^227462+3102)/2	68473	Stefano Morozzi	01/2020
9948	3^143497+8	68466	Lelio R Paula	04/2012
9949	2^227430-95	68464	Lelio R Paula	02/2012
9950	(8*10^68455+13)/3	68456	Robert Price	11/2017
9951	3*5^97934-2	68454	Lelio R Paula	09/2014
9952	20^52613+77	68452	Lelio R Paula	09/2013
9953	2^227371+32769	68446	Lelio R Paula	04/2012
9954	(3^143465+4)/21270420067	68440	Lelio R Paula	04/2012
9955	CopelandErdos(68433)	68433	Eric W. Weisstein	08/2013
9956	2^227323+75431	68432	Enzo Doria	04/2016
9957	2^227314-1965	68429	Lelio R Paula	04/2012
9958	2^227303-110617	68426	Enzo Doria	05/2014
9960	7^80963+66	68422	Lelio R Paula	07/2013
9959	2^227290+73849	68422	Enzo Doria	04/2016
9961	(14^59693-1)/13	68415	Paul Bourdelais	06/2008
9962	(1838^20959-1)/1837	68415	Serge Batalov	08/2020
9963	2^227256-2786249	68411	Enzo Doria	03/2016
9965	8*10^68400-7	68401	Dmitry Domanov	11/2010
9964	(15*2^227228-1)/583	68401	Lelio R Paula	01/2014
9966	2^227210+1869169	68398	Enzo Doria	05/2016
9967	(2^227176+2958)/2	68387	Stefano Morozzi	01/2020
9968	2^227159-1838635	68382	Enzo Doria	05/2015
9969	44*10^68368+3	68370	Robert Price	08/2017
9970	2^227115-7807	68369	Lelio R Paula	10/2009
9971	18469^5032+5032^18469	68368	Hans Havermann	08/2019
9972	2^227078-47355	68358	Lelio R Paula	04/2012
9973	16927^10920+10920^16927	68355	Hans Havermann	10/2019
9974	(2^227063-1017)/349	68351	Lelio R Paula	04/2012
9975	2^227057+148091	68351	Lelio R Paula	04/2012
9976	2^227046+187	68348	Lelio R Paula	02/2012
9977	(2^227030+454)/2	68343	Stefano Morozzi	01/2020
9978	(2^227022+2950)/2	68341	Stefano Morozzi	01/2020
9980	2^227009-4693	68337	Yves Minet	05/2019
9979	(2^227010+3214)/2	68337	Stefano Morozzi	01/2020
9981	9*10^68331+59	68332	Robert Price	10/2017
9982	11^65608-720	68324	Enzo Doria	11/2012
9983	(32*10^68320+319)/9	68321	Robert Price	10/2017
9984	33408!2-2^33408-1	68315	Joe McLean	05/2017
9985	2*10^68311-91	68312	Robert Price	04/2020
9986	2^226894-123	68302	Lelio R Paula	02/2012
9987	10^68297+141559	68298	Patrick De Geest	05/2013
9988	10^68297-93	68297	Robert Price	05/2011
9989	680^24107-679^24107	68284	Jean-Louis Charton	07/2010
9990	12^63267+59	68277	Lelio R Paula	07/2013
9991	2^226785-1159	68270	Yves Minet	11/2012
9992	7^80769+90	68258	Lelio R Paula	07/2013
9993	(88*10^68256-1)/3	68258	Robert Price	10/2017
9994	2^226741+66587	68256	Yves Minet	10/2010
9995	2^226720-112403	68250	Enzo Doria	06/2014
9996	(78557*2^226694+1)/3	68247	Lelio R Paula	06/2014
9997	(2^226665+1674)/2	68233	Stefano Morozzi	01/2020
9998	(83*10^68231+7)/9	68232	Robert Price	10/2015
9999	65^37636+16	68231	Lelio R Paula	01/2016
10000	5^97615-4^(97615+1)	68230	Robert Price	04/2016

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PRP Records

Probable Primes Top 10000

(271023 PRPs in the top)